Two coherent monochromatic beams of intensities $I$ and $4 I$ respectively are superposed. The maximum and minimum intensities in the resulting pattern are:

5 I

and

3 I

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9 I

and

3 I

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4 I

and

I

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9 I

and

I

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Solution

The correct option is D $9 I$ and $I$
Given : $I_{1} = 4 I$ $I_{2} = I$

Maximum intensity $I_{m a x} = (\sqrt{I_{1}} + \sqrt{I_{2}})^{2}$

$I_{m a x} = (\sqrt{4 I} + \sqrt{I})^{2}$ $= (2 \sqrt{I} + \sqrt{I})^{2} = (3 \sqrt{I})^{2} = 9 I$

Minimum intensity $I_{m i n} = (\sqrt{I_{1}} - \sqrt{I_{2}})^{2}$

$I_{m i n} = (\sqrt{4 I} - \sqrt{I})^{2}$ $= (2 \sqrt{I} - \sqrt{I})^{2} = (\sqrt{I})^{2} = I$

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